By asking what happened when space, food, or water did limit population growth, students could see the biological and mathematical consequences of assumptions.
Of particular importance was the assessment of the consequences of assumptions used in M&S: assumptions can be violated (e.g., addressed by additional evidence or a better model), mitigated (e.g., by label restriction, treatment regimen adjustment) or managed as potential risks for patients, regulators or sponsors.
This fact is a consequence of assumption (A.3)(a).
The uniqueness of the common fixed point is a consequence of assumption (F2).
Estimate (19) is purely a consequence of Assumption A via Remark 4. [2, Proposition 5.1].
This is in turn a consequence of assumption (3) in Definition 144.
Estimate (19) is purely a consequence of Assumption A via Remark 4. [2, Proposition 5.1] In this proposition, it is shown that there exists C such that if (Pi _y u,r ge C) then begin{aligned} lambda _{r/2}^{1/2}le frac{tilde{C}}{Vert Pi _y u,r Vert _{L^infty (B_1)}}lambda _{r}^{1/2} end{aligned} (20) for some (tilde{C}>0).
Using assumption (12) on Φ, we obtain that for all u ∈ , there exists r u ∈ ( σ, u ) such that ∫ σ + ∞ P ( s ) I s < u Φ ( s, u ) d s ≤ θ P ( r u ) ≤ θ B P ( u ), the second inequality being a consequence of assumption (25) on P. We deduce that there exists a constant C such that ∫ σ ∞ P ( s ) | m ( s, t ) | d s ≤ C ∫ 0 + ∞ P ( s ) ( | M ( s, t ) | + | J ( s, t ) | ) d s. (27).
The consequence of assumptions about dose levels depends on another assumption, the dose response: the increase in cancer for each unit increase in radiation dose.
The consequences of this assumption are evaluated in the next section.
Prior to interpreting Eqs. 10 or 11 as a complete power spectrum, and not as representing the energy of one particular set of basis functions, some investigations are required on the consequences of this assumption.
